I think the liar's paradox is not a complete statement and it will make sense of the sentence only when stated along with a preceding sentence/statement, which will completely state or explain what is the word 'This' is referring to.

Once the sentence or statement to which the word -'This' is referring to is well established, only then can the Liar's statement be understood and the statement would be true or false based on what the sentence to which the word- 'This' is referring to, is stating.

I don't think the Liar's paradox is complete, a good English grammatician can be consulted for understanding the sentence.

Simply considering the sentence, 'This statement is false' as a complete statement, and assuming that the word-'This' is pointing to the same sentence/statement, is an illogical understanding & interpretation of English & English Grammer.